Question

can you give me answer

Answer 1

Hey Mate

your answer is ----

firstly we find roots of 2x^2+x-1

2x^2+x-1 = 0

=> 2x^2+2x-x-1 = 0

=>2x(x+1) -(x+1) = 0

=> (x+1) (2x-1) = 0

=> x = 1/2 or -1

Let f(x) = 4x^4 -2x^3 -6x^2-x+ 1 is exactly divisible by 2x^2+x-1 only when

f(-1) = 0 or f(1/2) = 0

now , put x = 1 in f(x)
= 4×-1^4-2× -1^3 -6× -1^2 -1 +1

= 4+2 - 6 -1 +1

= 6 -6

=0

so, f(-1) = 0

hence, f(x) = 4x^4 -2x^3 -6x^2-x+ 1 is exactly divisible by 2x^2+x-1

HOPE IT HELPS YOU